molecular recognition and band alignment in 3-d covalent
TRANSCRIPT
doi.org/10.26434/chemrxiv.10792877.v2
Molecular Recognition and Band Alignment in 3-D Covalent OrganicFrameworks for Co-Crystalline Organic PhotovoltaicsJordan M Cox, Bradley Mileson, Ananthan Sadagopan, Steven Lopez
Submitted date: 24/03/2020 • Posted date: 24/03/2020Licence: CC BY-NC-ND 4.0Citation information: Cox, Jordan M; Mileson, Bradley; Sadagopan, Ananthan; Lopez, Steven (2019):Molecular Recognition and Band Alignment in 3-D Covalent Organic Frameworks for Co-Crystalline OrganicPhotovoltaics. ChemRxiv. Preprint. https://doi.org/10.26434/chemrxiv.10792877.v2
Covalent organic frameworks (COFs) have emerged as versatile, functional materials comprised of low-costmolecular building blocks. The permanent porosity, long-range order, and high surface area of 3D-COFspermit co-crystallization with other materials driven by supramolecular interactions. We designed a newsubphthalocyanine-based 3-D covalent organic framework (NEUCOF1) capable of forming co-crystals withfullerene (C60) via periodic ball-and-socket binding motifs. The high co-crystalline surface area andlong-range order of NEUCOF1 eliminates the typical surface area vs. structural order trade-off in organicphotovoltaics (OPVs). We used plane-wave density functional theory (PBE) to minimize NEUCOF1 andNEUCOF1–C60 co-crystals and determine their electronic band structures. Molecular dynamics (MD)simulations showed that NEUCOF1–C60 is likely to be stable up to 350 K. The band structures at 0 and 350 Ksuggest that charge transfer to the C60 acceptors is favorable and that directional charge transport is possiblefor these co-crystalline OPVs.
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Molecular Recognition and Band Alignment in 3-DCovalent Organic Frameworks for Co-Crystalline
Organic Photovoltaics
Jordan M. Cox‡, Bradley Mileson‡, Ananthan Sadagopan‡, Steven A. Lopez‡*
‡Department of Chemistry and Chemical Biology, Northeastern University, 805 ColumbusAvenue, ISEC 355, Boston, MA 02120
Abstract: Covalent organic frameworks (COFs) have emerged as versatile, functional materialscomprised of low-cost molecular building blocks. The permanent porosity, long-range order, andhigh surface area of 3D-COFs permit co-crystallization with other materials driven bysupramolecular interactions. We designed a new subphthalocyanine-based 3-D covalent organicframework (NEUCOF1) capable of forming co-crystals with fullerene (C60) via periodic ball-and-socket binding motifs. The high co-crystalline surface area and long-range order ofNEUCOF1 eliminates the typical surface area vs. structural order trade-off in organicphotovoltaics (OPVs). We used plane-wave density functional theory (PBE) to minimizeNEUCOF1 and NEUCOF1–C60 co-crystals and determine their electronic band structures.Molecular dynamics (MD) simulations showed that dispersive interactions promoting co-crystallinity NEUCOF1–C60 are stable up to 350 K. The band structures at 0 and 350 K suggestthat there is a driving force of 0.27 eV for exciton charge transfer to the pocket-bound fullerenes.Charge separation could then occur at the COF-C60 D-A interface, followed by the transfer of thefree electron to the nanowire of C60 acceptors with a driving force of 0.20 eV.
Introduction
Highly efficient photovoltaic (PV) technologies which harness the Sun’s energy could hold thekey to simultaneously eliminating reliance on fossil fuels and preventing further damage to theclimate. Unlike inorganic and perovskite solar cells, organic photovoltaics (OPVs) areconstructed from low-cost Earth-abundant materials and feature straightforward devicefabrication.1-2 However, current power conversion efficiencies (PCEs) in OPV devices exceedonly 14% and 17% for single junction and tandem devices, respectively, and have plateaued inrecent years.3-4 PCEs in current OPV devices are thought to be limited by the active layer
architecture due to the competition between structural order and donor-acceptor surface area,where charge separation occurs. The planar heterojunction (PHJ) architecture maximizesstructural order but has minimal D-A surface area, limiting the opportunities for chargeseparation. Bulk heterojunction (BHJ) devices blend the donor and acceptor materials, increasingtheir interfacial surface area while substantially reducing long-range order. This increases chargerecombination via local charge traps and substantially reduces directional free-charge diffusionpathways.5 Overcoming this PCE plateau is possible by continuing to develop the nascent co-crystalline OPV architecture that simultaneously maximizes both long-range order and D-Asurface area.
One class of materials of particular interest as electron-donating scaffolds in co-crystallineOPVs are covalent organic frameworks (COFs). COFs were first reported by Yaghi and co-workers;6 they are an exceptional class of permanently porous materials comprised of organic,synthetically accessible building blocks linked together in at least two dimensions. Oftenarranged in dispersion-bound 2D sheets, COFs exhibit empty channels formed by the alignedpores of adjacent sheets. Many examples of 2D COFs, and some 3D COFs, have been recentlyapplied to separations7-8, catalysis9-11, and organic electronics12-14, including OPVs,15-16 and havebeen the subject of rigorous computational study.17-21 Bein and co-workers reported the first COFOPV device; they demonstrated that charge-separation could be achieved from the electronicallyexcited COF to guest fullerene derivatives.22 A landmark study by Jiang and co-workers reportedthe highest PCE for a COF-based OPV measured to date, 0.9%.23 Despite the improvementsmade by Jiang and co-workers, PCEs in COF OPVs are still low. This is due in part to acombination of limited electronic communication between adjacent dispersion-bound COFsheets and poor molecular recognition between the planar COF sheets and curved fullereneacceptors. While COF co-crystals have emerged as a new OPV architecture, next-generation co-crystals will feature 3D-COFs to enhance structural order and molecular recognition of acceptormolecules.
A design strategy that could simultaneously improve both of these factors in COF OPVs is theincorporation of non-planar π-conjugated molecular building blocks.24 Non-planar π-conjugatedmolecules are known to recognize fullerenes in solution and various co-crystals have beenpublished.25-27 Their complementary shapes promote dispersion complexation through extendedπ-orbital overlap. Additionally, non-planar systems facilitate the formation of 3-D periodic COFmaterials, increasing the electronic coupling between adjacent COF sheets through covalentbonds. Inspired by this concept, we have designed a light-responsive, synthetically-accessible 3-
Figure 1. (Left) Chemical structure of a SubPc molecule with highlighted peripheral (blue X, green Y) and axial (red Z) positions. (Right) DFT-optimized geometry.
D COF, NEUCOF1, based on non-planar π-conjugated boron-subphthalocyanine (SubPcs,Figure 1) building blocks. These have well-documented syntheses and functionalization atperipheral and axial sites. Their absorption maximum ranges from 550-600 nm, making themideal candidates to absorb sunlight.28 SubPcs have been incorporated into several BHJ OPVdevices29-31 because of their ability to form dispersion complexes with C60 molecules in a ball-and-socket motif, in 1:1 and 2:1 ratios.25, 32-33 These complexes are also well known to undergocharge-transfer upon light absorption by SubPc to the dispersion-bound C60, further supportingour choice to pursue SubPc-based co-crystalline COFs.34-35 NEUCOF1 is a 3-D COF materialentirely comprised of periodically linked functionalized SubPc molecules. Ong and Swagerrecently demonstrate the self-correcting synthesis of thianthrene-based COFs via thecondensation of 1,2-dithiols and 1,2-difluoro compounds.36 This chemistry could possibly beextended to NEUCOF1 because of the intended thianthrene-like connection. Computational Methods
PW-DFT calculations were performed using the projector-augmented wave (PAW) methodwith the PBE exchange-correlation functional as implemented in the Vienna Ab initio SimulationPackage (VASP).37-40 A kinetic energy cutoff of 400 eV was used with a 2x2x2 Monkhorst-Packk-point grid and Grimme’s D3 empirical dispersion correction with Becke-Johnson damping.41
Initial models of NEUCOF1 and COF-C60 co-crystals were relaxed using a variable cellalgorithm until forces were less than 0.02 eV Å-1 per atom, and band structures, densities-of-states (DOS), and Γ-point partial charge densities were computed for these relaxed structures.DFT methods qualitatively reproduce band structures in semiconductor materials with theexception that the absolute value of the band gap is categorically underestimated, known as theband gap problem.42 Therefore, the computed PBE band structures discussed herein areinterpreted qualitatively, without relying on the value of the band gap energy. The band structuresfor all models were calculated along the high-symmetry path for hexagonal cells determined bySetyawan and Curtarolo (see SI).43 Partial charge densities and the band structure high-symmetrypath were visualized using the VESTA 3D visualization package.44 DOSs were computed on amore dense 6x6x6 k-point grid.
We estimated the band gap energy of NEUCOF1 by computing the energy gap between thehighest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital(LUMO) for oligomeric fragments of the COF. To this end, we used the hybrid density functionalB3LYP45 with the aug-cc-PVDZ46-48 basis set. The HOMO-LUMO gap for a single SubPcmonomer as well as a dimer, trimer, and tetramer were computed and plotted as a function of1/N, where N is the number of monomer units. This data was fit to a linear function andextrapolated to infinite monomers.
Molecular dynamics simulations were performed with the LAMMPS molecular dynamicsprogram49 using the OPLS3 all-atom force field.50 Models were initially relaxed at 10 K, thenheated over 100 ps to 350 K. After heating, the simulations were propagated for 2 ns and thestability of these simulations was determined by RMSD analysis, shown in the Supporting
Information. All final structures are based on the 2 ns production runs with the canonical (NVT)ensemble. Simulations were performed on three different co-crystalline models. Two of thesemodels utilize a truncated NEUCOF1 model which includes a single unidirectional channel andmaximizes the available surface area in the other two directions, resulting in a 1D wire analogueof NEUCOF1, see the Supporting Information. The 1D wire analogue allows our simulations toprobe the interactions of the COF with acceptor molecules near the surface. The other simulationuses a fully 3-D periodic model equivalent to the model of co-crystal C, described below. Fullsimulation details are provided in the Supporting Information.
Results and DiscussionWe have employed plane-wave density functional theory (PW-DFT) calculations to minimize
the periodic structure of NEUCOF1 (Figure 2). NEUCOF1 exhibits regular 17.4 Å bindingpockets, suitable for fullerene or other acceptor molecules, which are formed between adjacent
COF sheets. The sheets are linked by alkynyl connectors and are typically spaced by 4.3 Å (B−Bdistance) in the optimized structures. The COF also exhibits 17.9 Å unidirectional channelsformed by the alignment of the hexagonal pores in each sheet. These two types of binding sites,pockets and pores, are well suited to accommodate C60 molecules which have a van der Waalsdiameter of approximately 10 Å. To probe the interactions of NEUCOF1 with fullerene C60
guests, we have also minimized the geometries of three COF-C60 co-crystals, A, B, and C. Figure3 shows the PW-DFT relaxed unit cells of these co-crystals and illustrates the arrangement offullerenes in each co-crystal.
Figure 2. PW-DFT relaxed geometry of NEUCOF1. Views (left) along and (right) orthogonal to the hexagonal channels are shown and correspond to crystallographic directions [001] and [010] in the approximately hexagonal lattice. Widths of hexagonal pores, binding pockets, and sheet spacing are shown in red. Distances are reported in Ångstroms.
Co-crystal A contains fullerene molecules in the hexagonal channels, B contains fullerenes inthe binding pockets, and C has fullerenes in both binding sites. Figure 4 shows the periodicstructures of A, B, and C viewed down the hexagonal channel of the COF to illustrate thelocations of the acceptor molecules in the fully periodic models. Figure 4 also shows anorthogonal view of B to demonstrate the arrangement of fullerenes in the binding pockets. Theinteratomic spacing between C60 molecules in C is important to note here. The two uniquepocket-bound fullerene molecules in C and their respective nearest neighbor fullerene in the COFchannel are 3.1 and 3.0 Å apart. The two unique fullerene molecules in the channel are separatedby 2.8 Å.
Electronic structure
Figure 4. PW-DFT minimized geometries of A, B, and C. (a) View down the hexagonal channel of A, along crystallographic direction [001]. (b) View along [001] of B. (c) View along [001] of C. (d) View orthogonal to [001] of B, showing fullerene molecules held in the binding pockets, along crystallographic direction [010].
Figure 3. PW-DFT relaxed unit cells for co-crystals (a) A, (b) B, and (c) C.
To determine the suitability of NEUCOF1 for photovoltaic applications, we computed theband structures of the COF, and co-crystals A, B, and C. The band structures and correspondingDOS are shown in Figure 5. According to its band structure, NEUCOF1 is an organicsemiconductor with an indirect PBE band gap of 1.36 eV, though it is well known that PBEunderestimates this value. A hybrid DFT functional could improve our calculation of the bandgap energy, but the computational cost of hybrid DFT methods can be as much as three orders ofmagnitude greater in the case of PW-DFT. With a 9,700 Å3 unit cell and the 164-404 atoms in thecell, the cost of a hybrid-PW-DFT calculation is prohibitive. Botti and co-workers51 determinedthat the PBE functional underestimates band gaps by a median value of 0.8 eV. We estimate thetrue gap energy to be 2.2 eV for NEUCOF1 by applying the 0.8 eV correction. We also estimatedthe true gap energy by computing the HOMO-LUMO gap energy with hybrid-DFT for fourNEUCOF1 clusters featurign one to four SubPc units; a linear fit of these energies estimates aCOF band gap energy of 2.25 eV (Figure S4). PBE predicts that the valence band has a width of0.37 eV and the conduction band that has a width of 0.28 eV. This decreased band width suggeststhat electrons in the COF conduction band should be more localized than in the valence band.
Figure 5. Band structures and densities-of-states plots for (top-left) NEUCOF1 and co-crystals (top-right) A, (bottom-left) B, and (bottom-right) C. All energies are plotted relative to the Fermi level, shown by the red line, and vertical dashed lines show high-symmetry points. The DOS plots are separated into contributions from the COF (blue), fullerenes in binding pockets (grey), and fullerenes in channels (red).
The band structure of A illustrates the new energy bands resulting from the inclusion offullerenes into the COF channel. The fullerene conduction band (red DOS curve) is composed ofsix electronic bands which arise from the mixing of the three degenerate LUMOs on each of thetwo fullerene molecules in the unit cell, and lies within the band gap of the COF. The maximumof the fullerene conduction band lies 0.37 eV below the COF conduction band minimum. Thisband has a width of 0.20 eV; the conduction band width in crystalline C60 is approximately 0.5eV. The fullerene molecules in A should be isoenergetic, so the separation and spreading of theirbands indicates that these fullerene molecules are interacting with one another in the co-crystal.This column of interacting fullerenes could form a 1-D nanowire in NEUCOF1 co-crystals andrelated co-crystals.
The band structure and DOS of B shows the fullerene-localized conduction band in theband gap region of NEUCOF1, similar to A, 0.38 eV below the COF conduction band minimum.However, the six degenerate bands here are very flat, with a width of 0.03 eV. The fullerenemolecules in B are housed within the binding pockets of NEUCOF1, simultaneouslyquarantining each fullerene and preserving the degeneracy.
Co-crystal C combines the fullerene arrangements of A and B, and its band structure reflectsthis with contributions from twelve empty C60 orbitals in the conduction band group. Theconduction band width for fullerenes in C is 0.36 eV, and the conduction band maximum in thisgroup lies 0.27 eV below the COF conduction band, within the COF band gap. The width of 0.36eV indicates the presence of significantly delocalized orbitals involving all C60 molecules in thecell. The DOS shows that the bands at the top of this group are comprised of states more heavilylocalized on the pocket fullerenes (grey curve), while the lower-energy bands are more localizedon the channel fullerenes (red curve).
These band structures and DOS plots show that the electronic structure of NEUCOF1 islargely unchanged upon inclusion of fullerene acceptors into the framework. The conductionbands of the fullerenes are aligned well with the band gap of the COF and provide an energeticdriving force for NEUCOF1 → C60 charge transfer. The widths of the C60 conduction bands in Aand C (0.20, 0.27 eV) indicate a significant degree of orbital overlap between adjacent C60
molecules in the COF pores. The relatively close contacts of fullerenes (≤ 3.2 Å) and thedelocalized bands suggest that charge-hopping between C60 molecules is a possible mechanism ofcharge transport in the COF. Γ-point partial charge densities
To develop a chemically intuitive understanding of the electronic structure of NEUCOF1 andits C60 co-crystals, we have computed band-specific partial charge densities at the Γ-point for themost relevant frontier energy bands in NEUCOF1, A, B, and C. Figure 6 shows the densities forC; the corresponding densities for NEUCOF1, A, and B are nearly identical and are shown inTable S1 of the Supporting Information. The Γ-point densities show that the top valence band ismade up of the delocalized π-system of one of the COF sheets. This band is degenerate withanother valence band (not shown) which is comprised of the π-system of the other COF sheet in
the unit cell. The COF conduction band shows a depletion of electron density, relative to thevalence band, at the periphery of the SubPc units (i.e., near the sulfur atoms) with a localizationof this density around the cores of the SubPcs (i.e., near the nitrogen atoms). This localization ofdensity was seen in the band structures in the reduced band width of the COF conduction bandrelative to the valence band.
The Γ-point density for the fullerene conduction band maximum shows shared density betweenone pocket-bound fullerene and one channel fullerene. This delocalized electron density indicatesthe presence of significant intermolecular orbital overlap. The density localized on the pocket-bound fullerene in this partial charge density overlaps significantly with the density of the COFconduction band. This high degree of overlap promotes charge transfer from the COF to C60
molecules in the binding pockets, just as it does in SubPc-C60 molecular complexes.25, 34-35 Thus
Figure 6. Γ-point partial charge densities for frontier bands in C. (Bottom-left) Valence band, (bottom-right) fullerene conduction band minimum, (top-right) fullerene conduction band maximum, and (top-left) the COF conduction band minimum.
excitation of the COF should generate a COF-localized exciton which will experience a 0.27 eVdriving force for charge transfer to a fullerene acceptor in a nearby binding pocket.
The C60 conduction band minimum density shows shared electron density between the twofullerene molecules in the channel, forming a 1-D fullerene wire within the channel of the COF.The 0.20 eV width of the C60 conduction band provides an energetic driving force for anyelectrons in the C60 conduction band to relax to the lower band. This means that excited electrondensity in the pocket-bound fullerene orbitals would initially delocalize across the adjacent porefullerene, and subsequently localize onto the channel fullerenes. Combined with the initialdriving force for charge transfer, this additional force would promote charge separation at theCOF-C60 interface as well as transfer of the free electron into the 1-D fullerene wire in the nearbychannel.
Molecular dynamics simulationsThe structural stability of NEUCOF1-C60 dispersion-bound complexes at OPV operatingconditions is crucial to the ability of these co-crystals to act as OPV materials. The PW-DFTcalculations described above were performed on idealized 0 K structures, but OPVs operate atelevated temperatures. To determine this stability, we have employed molecular dynamicssimulations on three NEUCOF1-C60 model systems. In the first of these simulations, fullerenemolecules were placed into each of the binding pockets of the NEUCOF1 1-D wire analoguedescribed in the Computational Methods section, and a 2 ns NVT simulation was propagated at350 K, above typical OPV operating temperatures. At this temperature the C60 molecules remainwithin their binding pockets (Figure 7), which suggests that the dispersion intermolecular forcesare held between the fullerenes and the framework. The second simulation was performed on the3-D periodic model of C, with fullerene molecules in all of the binding pockets as well as thechannel sites. The NVT simulation of this co-crystal at 350 K shows similar results to those ofthe wire simulation. The C60 molecules housed in the binding pockets remain in those pocketsthroughout the simulation. Additionally, the channel fullerenes associate with the pocket-boundmolecules and form a fullerene network throughout the COF. Of particular note in this simulationis the short distance between all four of the fullerene molecules in the cell; the largest of thesedistances is 3.5 Å while non-covalent π-π interactions have been observed at distances up to 5.0Å.52 Therefore, all of the fullerene molecules in the simulation are near enough to participate in aconductive fullerene network.
We performed a third MD simulation on the NEUCOF1 1-D wire analogue to determinethe ability of NEUCOF1 to adsorb fullerene guests into its binding pockets. The model for thissimulations includes twelve fullerene molecules with six available binding pockets per cell toensure that some fullerenes would be left over after all of the binding pockets were filled. TheNEUCOF1 1-D wire empty and fullerenes are distributed in the surrounding void space as
shown in Figure 8.
Figure 8. Snapshots of (left) initial and (right) final configurations of 1-D wire analogue of NEUCOF1 in a fullerene-filled environment, viewed along pore direction, [001].
Figure 7. Snapshots of (left) initial and (right) final configurations of NEUCOF1 MD simulations at 350 K viewed along the pore direction, [001]. (Top) 1D wire analogue of NEUCOF1 with filled binding pockets, (bottom) co-crystal C.
Another 2 ns NVT simulation shows that these fullerenes migrate from their initial positionsinto the binding pockets of NEUCOF1. The thianthrene linkage promotes structural flexibility toreorganize as the fullerenes are accommodated. This simulation shows that these additionalfullerene molecules will bind fullerenes in empty peripheral pockets via π−π interactions.
Disorder effects on electronic structureWhile MD simulations show that the COF-C60 co-crystals are predicted to be stable from 0–
350 K, they also show a significant increase in structural disorder. We computed the bandstructure to determine the effect of thermal fluctuations on the electronic structure relative to the0 K structures. Figure 9 shows the computed band structure of C post-MD simulation. Thefullerene conduction band group in this disordered structure has a width of 0.36 eV, the same asfor C at 0 K. Some of the individual bands appear to flatten out at higher temperature, whichsuggests that the orbitals are more localized onto individual molecules than in the 0 K structure,while the 0.36 eV width suggests that the fullerenes are still interacting. Therefore, thermaleffects have a minor effect on the band structure and the co-crystal maintains its desirableelectronic structure at typical operating temperatures.
ConclusionsWe have designed a new SubPc-based COF (NEUCOF1) to function as an electron-donating
scaffold for next-generation co-crystalline OPV devices. NEUCOF1 can dock fullerene C60
acceptors and binds them in a ball-and-socket motif via its 17.4 Å binding pockets and theadjacent 17.9 Å unidirectional channels, likely to form COF-C60 co-crystals. We used PW-DFTmethods to minimize the geometries of NEUCOF1 and three COF-C60 co-crystals. The structuralstability of the COF-C60 co-crystals was assessed using MD simulations, which show thatfullerenes in the binding pockets remain dispersion-bound up to at least 350 K and maintainfavorable interaction distances within the C60 nanowire. Our computed band structures at 0K and
Figure 9. Band structure plot for final configuration of MD simulation of co-crystal C. Energy is plotted relative to the Fermi level, shown by red line, and vertical dashed lines show high-symmetry points.
350 K are consistent with sunlight absorption followed by a series of downhill charge transferand charge separation processes resulting in photocurrent. Our calculations show a driving forceof 0.27 eV for exciton charge transfer to the pocket-bound fullerenes. Charge separation couldthen occur at the COF-C60 D-A interface, followed by the transfer of the free electron to thenanowire of C60 acceptors with a driving force of 0.20 eV. The high internal surface area of theCOF combined with directional charge transport via columns of acceptor molecules, couldovercome the competition between D-A surface area and long-range order in current OPVarchitectures. Due to the promising structural and electronic properties of this material, furthertheoretical characterization of a family of related COFs is underway, and experimental synthesisand characterization are forthcoming.
Acknowledgements. The authors acknowledge the Department of Chemistry & ChemicalBiology for financial support. The high-performance computing resourced provided by theMassachusetts Green High-Performance Computing Center (MGHPCC), and the NortheasternHigh Performance (Discovery cluster).
Author Contributions. S. A. Lopez conceived of the project and supervised the co-authorsobtaining the results and the analysis thereof. J. M. Cox wrote the majority of the manuscript,performed many of the quantum mechanical calculations of the optimized structures, and bandstructures. J. M. Cox assisted B. Mileson in the set-up and oversaw the analysis of the remainingquantum mechanical calculations of the optimized structures, band structures, and DOSs. J. M.Cox assisted A. Sadagopan in the set-up and oversaw the analysis of the molecular dynamicssimulations. All authors contributed to the manuscript.
Competing Interests statement. The authors declare no conflicts of interest.
Supporting Information. The Supporting Information is available free of charge and includes avisualization of high-symmetry k-path used for band structures, RMSD plots for MD simulations,orbital images, unit cells and fractional coordinates for PW-DFT models.
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